Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9512099 · Acta Physica Polonica B

Conformal Field Theory Approach to the Kondo Effect

Ian K. Affleck

Published Dec 12, 1995• 124 citations
arXivHTMLPDF

Abstract

Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem. In this review some earlier approaches to the Kondo problem are discussed, the needed material on boundary conformal field theory is developed and then this new method is applied to the multi-channel Kondo problem.

DOI
10.48550/arxiv.cond-mat/9512099

Related papers

Quantum Impurity Problems in Condensed Matter Physics

Ian K. Affleck

Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.

arXiv:0809.3474•Sep 20, 2008•35 citations

FIELD THEORY APPROACH TO CRITICAL QUANTUM IMPURITY PROBLEMS AND APPLICATIONS TO THE MULTI-CHANNEL KONDO EFFECT

Andreas W. W. Ludwig

A new, general approach to finding exact solutions of Quantum Impurity Problems is reviewed, in which a local quantum mechanical degree of freedom is coupled to an extended variable, having gapless excitations. The principle ideas, using Conformal Field Theory techniques, are demonstrated in the example of the Multi-Channel Kondo effect, which exhibits unusual non-Fermi-liquid behavior at low temperatures and which appears to be relevant for Heavy Fermion Materials. In particular, static and dynamic Green's functions as well as transport and pairing properties are calculated exactly at low temperatures. Quantum Impurity Problems provide realizations of non-trivial, fully interacting Conformal Field Theories.

International Journal of Modern Physics B•Feb 14, 1994•42 citations

Conformal Field Theory Approach to Quantum Impurity Problems

Ian K. Affleck

A brief review is given of a new method for studying the critical behavior of quantum impurity problems, based on conformal field theory techniques, which I developed with Andreas Ludwig. Some results on the overscreened Kondo problem are reviewed. It is shown that the simple open and periodic fixed points, which occur in quantum spin chain impurity models, are related to each other by fusion.

arXiv:cond-mat/9311054•Nov 23, 1993•0 citations

Kondo Problem and Related One-dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory

Satoshi Fujimoto, Norio Kawakami

We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.

arXiv:cond-mat/0408171•Journal of the Physical Society of Japan•Jan 1, 2005•3 citations

Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion Green’s function, self-energy, and resistivity

Ian K. Affleck, Andreas W. W. Ludwig

A conformal-field-theory approach has recently been developed for quantum-impurity problems including the ``overscreened'' multichannel Kondo model. We present the details of our calculation of the single-fermion Green's function. The universal zero-temperature resistivity and leading temperature-dependent term are derived. Effects of particle-hole symmetry breaking are included. We also give our perturbative proof of the ``g theorem'' governing the change in residual entropy under a renormalization-group flow between two boundary fixed points.

Physical review. B, Condensed matter•Sep 1, 1993•433 citations

Kondo effect in a Luttinger liquid: A boundary-conformal-field-theory approach

P. Durganandini

The Kondo problem in a Luttinger liquid has been studied recently using a poor-man's-scaling method. Here, the problem is formulated using the recent boundary-conformal-field-theory technique, which allows us to describe the critical points exactly. We recover the results for the specific heat and susceptibility calculated for low temperatures.

Physical review. B, Condensed matter•Apr 1, 1996•14 citations
Recently, a new approach, based on boundary conformal field theory, has been applied to a variety of quantum impurity problems in condensed matter and particle physics. A particularly enlightening example is the multi-channel Kondo problem. In this review some earlier approaches to the Kondo problem are discussed, the needed material on boundary conformal field theory is developed and then this new method is applied to the multi-channel Kondo problem.
Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of excitations. The results can also be implied to nanoscopic devices like quantum dots. In these lecture notes, I review this field, including the following topics: I. General Renormalization Group (RG) framework for quantum impurity problems: example of simplest Kondo model II. Multi-channel Kondo model III. Quantum Dots: experimental realizations of one and two channel Kondo models IV. Impurities in Luttinger liquids: point contact in a quantum wire V. Quantum impurity entanglement entropy VI. Y-junctions of Luttinger liquids VII. Boundary condition changing operators and the X-ray edge problem.
A new, general approach to finding exact solutions of Quantum Impurity Problems is reviewed, in which a local quantum mechanical degree of freedom is coupled to an extended variable, having gapless excitations. The principle ideas, using Conformal Field Theory techniques, are demonstrated in the example of the Multi-Channel Kondo effect, which exhibits unusual non-Fermi-liquid behavior at low temperatures and which appears to be relevant for Heavy Fermion Materials. In particular, static and dynamic Green's functions as well as transport and pairing properties are calculated exactly at low temperatures. Quantum Impurity Problems provide realizations of non-trivial, fully interacting Conformal Field Theories.
We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.
A conformal-field-theory approach has recently been developed for quantum-impurity problems including the ``overscreened'' multichannel Kondo model. We present the details of our calculation of the single-fermion Green's function. The universal zero-temperature resistivity and leading temperature-dependent term are derived. Effects of particle-hole symmetry breaking are included. We also give our perturbative proof of the ``g theorem'' governing the change in residual entropy under a renormalization-group flow between two boundary fixed points.